A comparison of skewed and orthogonal lattices in Gaussian wiretap channels

We consider lattice coset-coded transmissions over a wiretap channel with additive white Gaussian noise (AWGN). Examining a function that can be interpreted as either the legitimate receiver's error probability or the eavesdropper's correct decision probability, we rigorously show that, albeit offering simple bit labeling, orthogonal nested lattices are suboptimal for coset coding in terms of both the legitimate receiver's and the eavesdropper's probabilities.